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<div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno">    1</span>&#160;<span class="preprocessor">#include &quot;./InternalHeaderCheck.h&quot;</span></div>
<div class="line"><a name="l00002"></a><span class="lineno">    2</span>&#160; </div>
<div class="line"><a name="l00003"></a><span class="lineno">    3</span>&#160;<span class="keyword">namespace </span><a class="code" href="namespaceEigen.html">Eigen</a> { </div>
<div class="line"><a name="l00004"></a><span class="lineno">    4</span>&#160; </div>
<div class="line"><a name="l00005"></a><span class="lineno">    5</span>&#160;<span class="keyword">namespace </span>internal {</div>
<div class="line"><a name="l00006"></a><span class="lineno">    6</span>&#160; </div>
<div class="line"><a name="l00007"></a><span class="lineno">    7</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> Scalar&gt;</div>
<div class="line"><a name="l00008"></a><span class="lineno">    8</span>&#160;<span class="keywordtype">void</span> lmpar(</div>
<div class="line"><a name="l00009"></a><span class="lineno">    9</span>&#160;        <a class="codeRef" href="../classEigen_1_1Matrix.html">Matrix&lt; Scalar, Dynamic, Dynamic &gt;</a> &amp;r,</div>
<div class="line"><a name="l00010"></a><span class="lineno">   10</span>&#160;        <span class="keyword">const</span> <a class="codeRef" href="../group__matrixtypedefs.html#gaf20e523ca57ee8ef0a945cd4703d2bfd">VectorXi</a> &amp;ipvt,</div>
<div class="line"><a name="l00011"></a><span class="lineno">   11</span>&#160;        <span class="keyword">const</span> <a class="codeRef" href="../classEigen_1_1Matrix.html">Matrix&lt; Scalar, Dynamic, 1 &gt;</a>  &amp;diag,</div>
<div class="line"><a name="l00012"></a><span class="lineno">   12</span>&#160;        <span class="keyword">const</span> <a class="codeRef" href="../classEigen_1_1Matrix.html">Matrix&lt; Scalar, Dynamic, 1 &gt;</a>  &amp;qtb,</div>
<div class="line"><a name="l00013"></a><span class="lineno">   13</span>&#160;        Scalar delta,</div>
<div class="line"><a name="l00014"></a><span class="lineno">   14</span>&#160;        Scalar &amp;par,</div>
<div class="line"><a name="l00015"></a><span class="lineno">   15</span>&#160;        <a class="codeRef" href="../classEigen_1_1Matrix.html">Matrix&lt; Scalar, Dynamic, 1 &gt;</a>  &amp;x)</div>
<div class="line"><a name="l00016"></a><span class="lineno">   16</span>&#160;{</div>
<div class="line"><a name="l00017"></a><span class="lineno">   17</span>&#160;    <span class="keyword">using</span> std::abs;</div>
<div class="line"><a name="l00018"></a><span class="lineno">   18</span>&#160;    <span class="keyword">using</span> std::sqrt;</div>
<div class="line"><a name="l00019"></a><span class="lineno">   19</span>&#160;    <span class="keyword">typedef</span> DenseIndex <a class="codeRef" href="../namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a>;</div>
<div class="line"><a name="l00020"></a><span class="lineno">   20</span>&#160; </div>
<div class="line"><a name="l00021"></a><span class="lineno">   21</span>&#160;    <span class="comment">/* Local variables */</span></div>
<div class="line"><a name="l00022"></a><span class="lineno">   22</span>&#160;    <a class="codeRef" href="../namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> i, j, l;</div>
<div class="line"><a name="l00023"></a><span class="lineno">   23</span>&#160;    Scalar fp;</div>
<div class="line"><a name="l00024"></a><span class="lineno">   24</span>&#160;    Scalar parc, parl;</div>
<div class="line"><a name="l00025"></a><span class="lineno">   25</span>&#160;    <a class="codeRef" href="../namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> iter;</div>
<div class="line"><a name="l00026"></a><span class="lineno">   26</span>&#160;    Scalar temp, paru;</div>
<div class="line"><a name="l00027"></a><span class="lineno">   27</span>&#160;    Scalar gnorm;</div>
<div class="line"><a name="l00028"></a><span class="lineno">   28</span>&#160;    Scalar dxnorm;</div>
<div class="line"><a name="l00029"></a><span class="lineno">   29</span>&#160; </div>
<div class="line"><a name="l00030"></a><span class="lineno">   30</span>&#160; </div>
<div class="line"><a name="l00031"></a><span class="lineno">   31</span>&#160;    <span class="comment">/* Function Body */</span></div>
<div class="line"><a name="l00032"></a><span class="lineno">   32</span>&#160;    <span class="keyword">const</span> Scalar dwarf = (std::numeric_limits&lt;Scalar&gt;::min)();</div>
<div class="line"><a name="l00033"></a><span class="lineno">   33</span>&#160;    <span class="keyword">const</span> <a class="codeRef" href="../namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> n = r.cols();</div>
<div class="line"><a name="l00034"></a><span class="lineno">   34</span>&#160;    eigen_assert(n==diag.size());</div>
<div class="line"><a name="l00035"></a><span class="lineno">   35</span>&#160;    eigen_assert(n==qtb.size());</div>
<div class="line"><a name="l00036"></a><span class="lineno">   36</span>&#160;    eigen_assert(n==x.size());</div>
<div class="line"><a name="l00037"></a><span class="lineno">   37</span>&#160; </div>
<div class="line"><a name="l00038"></a><span class="lineno">   38</span>&#160;    <a class="codeRef" href="../classEigen_1_1Matrix.html">Matrix&lt; Scalar, Dynamic, 1 &gt;</a>  wa1, wa2;</div>
<div class="line"><a name="l00039"></a><span class="lineno">   39</span>&#160; </div>
<div class="line"><a name="l00040"></a><span class="lineno">   40</span>&#160;    <span class="comment">/* compute and store in x the gauss-newton direction. if the */</span></div>
<div class="line"><a name="l00041"></a><span class="lineno">   41</span>&#160;    <span class="comment">/* jacobian is rank-deficient, obtain a least squares solution. */</span></div>
<div class="line"><a name="l00042"></a><span class="lineno">   42</span>&#160;    <a class="codeRef" href="../namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> nsing = n-1;</div>
<div class="line"><a name="l00043"></a><span class="lineno">   43</span>&#160;    wa1 = qtb;</div>
<div class="line"><a name="l00044"></a><span class="lineno">   44</span>&#160;    <span class="keywordflow">for</span> (j = 0; j &lt; n; ++j) {</div>
<div class="line"><a name="l00045"></a><span class="lineno">   45</span>&#160;        <span class="keywordflow">if</span> (r(j,j) == 0. &amp;&amp; nsing == n-1)</div>
<div class="line"><a name="l00046"></a><span class="lineno">   46</span>&#160;            nsing = j - 1;</div>
<div class="line"><a name="l00047"></a><span class="lineno">   47</span>&#160;        <span class="keywordflow">if</span> (nsing &lt; n-1)</div>
<div class="line"><a name="l00048"></a><span class="lineno">   48</span>&#160;            wa1[j] = 0.;</div>
<div class="line"><a name="l00049"></a><span class="lineno">   49</span>&#160;    }</div>
<div class="line"><a name="l00050"></a><span class="lineno">   50</span>&#160;    <span class="keywordflow">for</span> (j = nsing; j&gt;=0; --j) {</div>
<div class="line"><a name="l00051"></a><span class="lineno">   51</span>&#160;        wa1[j] /= r(j,j);</div>
<div class="line"><a name="l00052"></a><span class="lineno">   52</span>&#160;        temp = wa1[j];</div>
<div class="line"><a name="l00053"></a><span class="lineno">   53</span>&#160;        <span class="keywordflow">for</span> (i = 0; i &lt; j ; ++i)</div>
<div class="line"><a name="l00054"></a><span class="lineno">   54</span>&#160;            wa1[i] -= r(i,j) * temp;</div>
<div class="line"><a name="l00055"></a><span class="lineno">   55</span>&#160;    }</div>
<div class="line"><a name="l00056"></a><span class="lineno">   56</span>&#160; </div>
<div class="line"><a name="l00057"></a><span class="lineno">   57</span>&#160;    <span class="keywordflow">for</span> (j = 0; j &lt; n; ++j)</div>
<div class="line"><a name="l00058"></a><span class="lineno">   58</span>&#160;        x[ipvt[j]] = wa1[j];</div>
<div class="line"><a name="l00059"></a><span class="lineno">   59</span>&#160; </div>
<div class="line"><a name="l00060"></a><span class="lineno">   60</span>&#160;    <span class="comment">/* initialize the iteration counter. */</span></div>
<div class="line"><a name="l00061"></a><span class="lineno">   61</span>&#160;    <span class="comment">/* evaluate the function at the origin, and test */</span></div>
<div class="line"><a name="l00062"></a><span class="lineno">   62</span>&#160;    <span class="comment">/* for acceptance of the gauss-newton direction. */</span></div>
<div class="line"><a name="l00063"></a><span class="lineno">   63</span>&#160;    iter = 0;</div>
<div class="line"><a name="l00064"></a><span class="lineno">   64</span>&#160;    wa2 = diag.cwiseProduct(x);</div>
<div class="line"><a name="l00065"></a><span class="lineno">   65</span>&#160;    dxnorm = wa2.blueNorm();</div>
<div class="line"><a name="l00066"></a><span class="lineno">   66</span>&#160;    fp = dxnorm - delta;</div>
<div class="line"><a name="l00067"></a><span class="lineno">   67</span>&#160;    <span class="keywordflow">if</span> (fp &lt;= Scalar(0.1) * delta) {</div>
<div class="line"><a name="l00068"></a><span class="lineno">   68</span>&#160;        par = 0;</div>
<div class="line"><a name="l00069"></a><span class="lineno">   69</span>&#160;        <span class="keywordflow">return</span>;</div>
<div class="line"><a name="l00070"></a><span class="lineno">   70</span>&#160;    }</div>
<div class="line"><a name="l00071"></a><span class="lineno">   71</span>&#160; </div>
<div class="line"><a name="l00072"></a><span class="lineno">   72</span>&#160;    <span class="comment">/* if the jacobian is not rank deficient, the newton */</span></div>
<div class="line"><a name="l00073"></a><span class="lineno">   73</span>&#160;    <span class="comment">/* step provides a lower bound, parl, for the zero of */</span></div>
<div class="line"><a name="l00074"></a><span class="lineno">   74</span>&#160;    <span class="comment">/* the function. otherwise set this bound to zero. */</span></div>
<div class="line"><a name="l00075"></a><span class="lineno">   75</span>&#160;    parl = 0.;</div>
<div class="line"><a name="l00076"></a><span class="lineno">   76</span>&#160;    <span class="keywordflow">if</span> (nsing &gt;= n-1) {</div>
<div class="line"><a name="l00077"></a><span class="lineno">   77</span>&#160;        <span class="keywordflow">for</span> (j = 0; j &lt; n; ++j) {</div>
<div class="line"><a name="l00078"></a><span class="lineno">   78</span>&#160;            l = ipvt[j];</div>
<div class="line"><a name="l00079"></a><span class="lineno">   79</span>&#160;            wa1[j] = diag[l] * (wa2[l] / dxnorm);</div>
<div class="line"><a name="l00080"></a><span class="lineno">   80</span>&#160;        }</div>
<div class="line"><a name="l00081"></a><span class="lineno">   81</span>&#160;        <span class="comment">// it&#39;s actually a triangularView.solveInplace(), though in a weird</span></div>
<div class="line"><a name="l00082"></a><span class="lineno">   82</span>&#160;        <span class="comment">// way:</span></div>
<div class="line"><a name="l00083"></a><span class="lineno">   83</span>&#160;        <span class="keywordflow">for</span> (j = 0; j &lt; n; ++j) {</div>
<div class="line"><a name="l00084"></a><span class="lineno">   84</span>&#160;            Scalar sum = 0.;</div>
<div class="line"><a name="l00085"></a><span class="lineno">   85</span>&#160;            <span class="keywordflow">for</span> (i = 0; i &lt; j; ++i)</div>
<div class="line"><a name="l00086"></a><span class="lineno">   86</span>&#160;                sum += r(i,j) * wa1[i];</div>
<div class="line"><a name="l00087"></a><span class="lineno">   87</span>&#160;            wa1[j] = (wa1[j] - sum) / r(j,j);</div>
<div class="line"><a name="l00088"></a><span class="lineno">   88</span>&#160;        }</div>
<div class="line"><a name="l00089"></a><span class="lineno">   89</span>&#160;        temp = wa1.blueNorm();</div>
<div class="line"><a name="l00090"></a><span class="lineno">   90</span>&#160;        parl = fp / delta / temp / temp;</div>
<div class="line"><a name="l00091"></a><span class="lineno">   91</span>&#160;    }</div>
<div class="line"><a name="l00092"></a><span class="lineno">   92</span>&#160; </div>
<div class="line"><a name="l00093"></a><span class="lineno">   93</span>&#160;    <span class="comment">/* calculate an upper bound, paru, for the zero of the function. */</span></div>
<div class="line"><a name="l00094"></a><span class="lineno">   94</span>&#160;    <span class="keywordflow">for</span> (j = 0; j &lt; n; ++j)</div>
<div class="line"><a name="l00095"></a><span class="lineno">   95</span>&#160;        wa1[j] = r.col(j).head(j+1).dot(qtb.head(j+1)) / diag[ipvt[j]];</div>
<div class="line"><a name="l00096"></a><span class="lineno">   96</span>&#160; </div>
<div class="line"><a name="l00097"></a><span class="lineno">   97</span>&#160;    gnorm = wa1.stableNorm();</div>
<div class="line"><a name="l00098"></a><span class="lineno">   98</span>&#160;    paru = gnorm / delta;</div>
<div class="line"><a name="l00099"></a><span class="lineno">   99</span>&#160;    <span class="keywordflow">if</span> (paru == 0.)</div>
<div class="line"><a name="l00100"></a><span class="lineno">  100</span>&#160;        paru = dwarf / (std::min)(delta,Scalar(0.1));</div>
<div class="line"><a name="l00101"></a><span class="lineno">  101</span>&#160; </div>
<div class="line"><a name="l00102"></a><span class="lineno">  102</span>&#160;    <span class="comment">/* if the input par lies outside of the interval (parl,paru), */</span></div>
<div class="line"><a name="l00103"></a><span class="lineno">  103</span>&#160;    <span class="comment">/* set par to the closer endpoint. */</span></div>
<div class="line"><a name="l00104"></a><span class="lineno">  104</span>&#160;    par = (std::max)(par,parl);</div>
<div class="line"><a name="l00105"></a><span class="lineno">  105</span>&#160;    par = (std::min)(par,paru);</div>
<div class="line"><a name="l00106"></a><span class="lineno">  106</span>&#160;    <span class="keywordflow">if</span> (par == 0.)</div>
<div class="line"><a name="l00107"></a><span class="lineno">  107</span>&#160;        par = gnorm / dxnorm;</div>
<div class="line"><a name="l00108"></a><span class="lineno">  108</span>&#160; </div>
<div class="line"><a name="l00109"></a><span class="lineno">  109</span>&#160;    <span class="comment">/* beginning of an iteration. */</span></div>
<div class="line"><a name="l00110"></a><span class="lineno">  110</span>&#160;    <span class="keywordflow">while</span> (<span class="keyword">true</span>) {</div>
<div class="line"><a name="l00111"></a><span class="lineno">  111</span>&#160;        ++iter;</div>
<div class="line"><a name="l00112"></a><span class="lineno">  112</span>&#160; </div>
<div class="line"><a name="l00113"></a><span class="lineno">  113</span>&#160;        <span class="comment">/* evaluate the function at the current value of par. */</span></div>
<div class="line"><a name="l00114"></a><span class="lineno">  114</span>&#160;        <span class="keywordflow">if</span> (par == 0.)</div>
<div class="line"><a name="l00115"></a><span class="lineno">  115</span>&#160;            par = (std::max)(dwarf,Scalar(.001) * paru); <span class="comment">/* Computing MAX */</span></div>
<div class="line"><a name="l00116"></a><span class="lineno">  116</span>&#160;        wa1 = <a class="codeRef" href="../namespaceEigen.html#af4f536e8ea56702e63088efb3706d1f0">sqrt</a>(par)* diag;</div>
<div class="line"><a name="l00117"></a><span class="lineno">  117</span>&#160; </div>
<div class="line"><a name="l00118"></a><span class="lineno">  118</span>&#160;        <a class="codeRef" href="../classEigen_1_1Matrix.html">Matrix&lt; Scalar, Dynamic, 1 &gt;</a> sdiag(n);</div>
<div class="line"><a name="l00119"></a><span class="lineno">  119</span>&#160;        qrsolv&lt;Scalar&gt;(r, ipvt, wa1, qtb, x, sdiag);</div>
<div class="line"><a name="l00120"></a><span class="lineno">  120</span>&#160; </div>
<div class="line"><a name="l00121"></a><span class="lineno">  121</span>&#160;        wa2 = diag.cwiseProduct(x);</div>
<div class="line"><a name="l00122"></a><span class="lineno">  122</span>&#160;        dxnorm = wa2.blueNorm();</div>
<div class="line"><a name="l00123"></a><span class="lineno">  123</span>&#160;        temp = fp;</div>
<div class="line"><a name="l00124"></a><span class="lineno">  124</span>&#160;        fp = dxnorm - delta;</div>
<div class="line"><a name="l00125"></a><span class="lineno">  125</span>&#160; </div>
<div class="line"><a name="l00126"></a><span class="lineno">  126</span>&#160;        <span class="comment">/* if the function is small enough, accept the current value */</span></div>
<div class="line"><a name="l00127"></a><span class="lineno">  127</span>&#160;        <span class="comment">/* of par. also test for the exceptional cases where parl */</span></div>
<div class="line"><a name="l00128"></a><span class="lineno">  128</span>&#160;        <span class="comment">/* is zero or the number of iterations has reached 10. */</span></div>
<div class="line"><a name="l00129"></a><span class="lineno">  129</span>&#160;        <span class="keywordflow">if</span> (<a class="codeRef" href="../namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">abs</a>(fp) &lt;= Scalar(0.1) * delta || (parl == 0. &amp;&amp; fp &lt;= temp &amp;&amp; temp &lt; 0.) || iter == 10)</div>
<div class="line"><a name="l00130"></a><span class="lineno">  130</span>&#160;            <span class="keywordflow">break</span>;</div>
<div class="line"><a name="l00131"></a><span class="lineno">  131</span>&#160; </div>
<div class="line"><a name="l00132"></a><span class="lineno">  132</span>&#160;        <span class="comment">/* compute the newton correction. */</span></div>
<div class="line"><a name="l00133"></a><span class="lineno">  133</span>&#160;        <span class="keywordflow">for</span> (j = 0; j &lt; n; ++j) {</div>
<div class="line"><a name="l00134"></a><span class="lineno">  134</span>&#160;            l = ipvt[j];</div>
<div class="line"><a name="l00135"></a><span class="lineno">  135</span>&#160;            wa1[j] = diag[l] * (wa2[l] / dxnorm);</div>
<div class="line"><a name="l00136"></a><span class="lineno">  136</span>&#160;        }</div>
<div class="line"><a name="l00137"></a><span class="lineno">  137</span>&#160;        <span class="keywordflow">for</span> (j = 0; j &lt; n; ++j) {</div>
<div class="line"><a name="l00138"></a><span class="lineno">  138</span>&#160;            wa1[j] /= sdiag[j];</div>
<div class="line"><a name="l00139"></a><span class="lineno">  139</span>&#160;            temp = wa1[j];</div>
<div class="line"><a name="l00140"></a><span class="lineno">  140</span>&#160;            <span class="keywordflow">for</span> (i = j+1; i &lt; n; ++i)</div>
<div class="line"><a name="l00141"></a><span class="lineno">  141</span>&#160;                wa1[i] -= r(i,j) * temp;</div>
<div class="line"><a name="l00142"></a><span class="lineno">  142</span>&#160;        }</div>
<div class="line"><a name="l00143"></a><span class="lineno">  143</span>&#160;        temp = wa1.blueNorm();</div>
<div class="line"><a name="l00144"></a><span class="lineno">  144</span>&#160;        parc = fp / delta / temp / temp;</div>
<div class="line"><a name="l00145"></a><span class="lineno">  145</span>&#160; </div>
<div class="line"><a name="l00146"></a><span class="lineno">  146</span>&#160;        <span class="comment">/* depending on the sign of the function, update parl or paru. */</span></div>
<div class="line"><a name="l00147"></a><span class="lineno">  147</span>&#160;        <span class="keywordflow">if</span> (fp &gt; 0.)</div>
<div class="line"><a name="l00148"></a><span class="lineno">  148</span>&#160;            parl = (std::max)(parl,par);</div>
<div class="line"><a name="l00149"></a><span class="lineno">  149</span>&#160;        <span class="keywordflow">if</span> (fp &lt; 0.)</div>
<div class="line"><a name="l00150"></a><span class="lineno">  150</span>&#160;            paru = (std::min)(paru,par);</div>
<div class="line"><a name="l00151"></a><span class="lineno">  151</span>&#160; </div>
<div class="line"><a name="l00152"></a><span class="lineno">  152</span>&#160;        <span class="comment">/* compute an improved estimate for par. */</span></div>
<div class="line"><a name="l00153"></a><span class="lineno">  153</span>&#160;        <span class="comment">/* Computing MAX */</span></div>
<div class="line"><a name="l00154"></a><span class="lineno">  154</span>&#160;        par = (std::max)(parl,par+parc);</div>
<div class="line"><a name="l00155"></a><span class="lineno">  155</span>&#160; </div>
<div class="line"><a name="l00156"></a><span class="lineno">  156</span>&#160;        <span class="comment">/* end of an iteration. */</span></div>
<div class="line"><a name="l00157"></a><span class="lineno">  157</span>&#160;    }</div>
<div class="line"><a name="l00158"></a><span class="lineno">  158</span>&#160; </div>
<div class="line"><a name="l00159"></a><span class="lineno">  159</span>&#160;    <span class="comment">/* termination. */</span></div>
<div class="line"><a name="l00160"></a><span class="lineno">  160</span>&#160;    <span class="keywordflow">if</span> (iter == 0)</div>
<div class="line"><a name="l00161"></a><span class="lineno">  161</span>&#160;        par = 0.;</div>
<div class="line"><a name="l00162"></a><span class="lineno">  162</span>&#160;    <span class="keywordflow">return</span>;</div>
<div class="line"><a name="l00163"></a><span class="lineno">  163</span>&#160;}</div>
<div class="line"><a name="l00164"></a><span class="lineno">  164</span>&#160; </div>
<div class="line"><a name="l00165"></a><span class="lineno">  165</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> Scalar&gt;</div>
<div class="line"><a name="l00166"></a><span class="lineno">  166</span>&#160;<span class="keywordtype">void</span> lmpar2(</div>
<div class="line"><a name="l00167"></a><span class="lineno">  167</span>&#160;        <span class="keyword">const</span> ColPivHouseholderQR&lt;Matrix&lt; Scalar, Dynamic, Dynamic&gt; &gt; &amp;qr,</div>
<div class="line"><a name="l00168"></a><span class="lineno">  168</span>&#160;        <span class="keyword">const</span> <a class="codeRef" href="../classEigen_1_1Matrix.html">Matrix&lt; Scalar, Dynamic, 1 &gt;</a>  &amp;diag,</div>
<div class="line"><a name="l00169"></a><span class="lineno">  169</span>&#160;        <span class="keyword">const</span> <a class="codeRef" href="../classEigen_1_1Matrix.html">Matrix&lt; Scalar, Dynamic, 1 &gt;</a>  &amp;qtb,</div>
<div class="line"><a name="l00170"></a><span class="lineno">  170</span>&#160;        Scalar delta,</div>
<div class="line"><a name="l00171"></a><span class="lineno">  171</span>&#160;        Scalar &amp;par,</div>
<div class="line"><a name="l00172"></a><span class="lineno">  172</span>&#160;        <a class="codeRef" href="../classEigen_1_1Matrix.html">Matrix&lt; Scalar, Dynamic, 1 &gt;</a>  &amp;x)</div>
<div class="line"><a name="l00173"></a><span class="lineno">  173</span>&#160; </div>
<div class="line"><a name="l00174"></a><span class="lineno">  174</span>&#160;{</div>
<div class="line"><a name="l00175"></a><span class="lineno">  175</span>&#160;    <span class="keyword">using</span> std::sqrt;</div>
<div class="line"><a name="l00176"></a><span class="lineno">  176</span>&#160;    <span class="keyword">using</span> std::abs;</div>
<div class="line"><a name="l00177"></a><span class="lineno">  177</span>&#160;    <span class="keyword">typedef</span> DenseIndex <a class="codeRef" href="../namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a>;</div>
<div class="line"><a name="l00178"></a><span class="lineno">  178</span>&#160; </div>
<div class="line"><a name="l00179"></a><span class="lineno">  179</span>&#160;    <span class="comment">/* Local variables */</span></div>
<div class="line"><a name="l00180"></a><span class="lineno">  180</span>&#160;    <a class="codeRef" href="../namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> j;</div>
<div class="line"><a name="l00181"></a><span class="lineno">  181</span>&#160;    Scalar fp;</div>
<div class="line"><a name="l00182"></a><span class="lineno">  182</span>&#160;    Scalar parc, parl;</div>
<div class="line"><a name="l00183"></a><span class="lineno">  183</span>&#160;    <a class="codeRef" href="../namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> iter;</div>
<div class="line"><a name="l00184"></a><span class="lineno">  184</span>&#160;    Scalar temp, paru;</div>
<div class="line"><a name="l00185"></a><span class="lineno">  185</span>&#160;    Scalar gnorm;</div>
<div class="line"><a name="l00186"></a><span class="lineno">  186</span>&#160;    Scalar dxnorm;</div>
<div class="line"><a name="l00187"></a><span class="lineno">  187</span>&#160; </div>
<div class="line"><a name="l00188"></a><span class="lineno">  188</span>&#160; </div>
<div class="line"><a name="l00189"></a><span class="lineno">  189</span>&#160;    <span class="comment">/* Function Body */</span></div>
<div class="line"><a name="l00190"></a><span class="lineno">  190</span>&#160;    <span class="keyword">const</span> Scalar dwarf = (std::numeric_limits&lt;Scalar&gt;::min)();</div>
<div class="line"><a name="l00191"></a><span class="lineno">  191</span>&#160;    <span class="keyword">const</span> <a class="codeRef" href="../namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> n = qr.matrixQR().cols();</div>
<div class="line"><a name="l00192"></a><span class="lineno">  192</span>&#160;    eigen_assert(n==diag.size());</div>
<div class="line"><a name="l00193"></a><span class="lineno">  193</span>&#160;    eigen_assert(n==qtb.size());</div>
<div class="line"><a name="l00194"></a><span class="lineno">  194</span>&#160; </div>
<div class="line"><a name="l00195"></a><span class="lineno">  195</span>&#160;    <a class="codeRef" href="../classEigen_1_1Matrix.html">Matrix&lt; Scalar, Dynamic, 1 &gt;</a>  wa1, wa2;</div>
<div class="line"><a name="l00196"></a><span class="lineno">  196</span>&#160; </div>
<div class="line"><a name="l00197"></a><span class="lineno">  197</span>&#160;    <span class="comment">/* compute and store in x the gauss-newton direction. if the */</span></div>
<div class="line"><a name="l00198"></a><span class="lineno">  198</span>&#160;    <span class="comment">/* jacobian is rank-deficient, obtain a least squares solution. */</span></div>
<div class="line"><a name="l00199"></a><span class="lineno">  199</span>&#160; </div>
<div class="line"><a name="l00200"></a><span class="lineno">  200</span>&#160;<span class="comment">//    const Index rank = qr.nonzeroPivots(); // exactly double(0.)</span></div>
<div class="line"><a name="l00201"></a><span class="lineno">  201</span>&#160;    <span class="keyword">const</span> <a class="codeRef" href="../namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> rank = qr.rank(); <span class="comment">// use a threshold</span></div>
<div class="line"><a name="l00202"></a><span class="lineno">  202</span>&#160;    wa1 = qtb;</div>
<div class="line"><a name="l00203"></a><span class="lineno">  203</span>&#160;    wa1.tail(n-rank).<a class="codeRef" href="../classEigen_1_1PlainObjectBase.html#acc39eaf7ba22b725c86f1b9b8bb57c3c">setZero</a>();</div>
<div class="line"><a name="l00204"></a><span class="lineno">  204</span>&#160;    qr.matrixQR().topLeftCorner(rank, rank).template triangularView&lt;Upper&gt;().solveInPlace(wa1.head(rank));</div>
<div class="line"><a name="l00205"></a><span class="lineno">  205</span>&#160; </div>
<div class="line"><a name="l00206"></a><span class="lineno">  206</span>&#160;    x = qr.colsPermutation()*wa1;</div>
<div class="line"><a name="l00207"></a><span class="lineno">  207</span>&#160; </div>
<div class="line"><a name="l00208"></a><span class="lineno">  208</span>&#160;    <span class="comment">/* initialize the iteration counter. */</span></div>
<div class="line"><a name="l00209"></a><span class="lineno">  209</span>&#160;    <span class="comment">/* evaluate the function at the origin, and test */</span></div>
<div class="line"><a name="l00210"></a><span class="lineno">  210</span>&#160;    <span class="comment">/* for acceptance of the gauss-newton direction. */</span></div>
<div class="line"><a name="l00211"></a><span class="lineno">  211</span>&#160;    iter = 0;</div>
<div class="line"><a name="l00212"></a><span class="lineno">  212</span>&#160;    wa2 = diag.cwiseProduct(x);</div>
<div class="line"><a name="l00213"></a><span class="lineno">  213</span>&#160;    dxnorm = wa2.blueNorm();</div>
<div class="line"><a name="l00214"></a><span class="lineno">  214</span>&#160;    fp = dxnorm - delta;</div>
<div class="line"><a name="l00215"></a><span class="lineno">  215</span>&#160;    <span class="keywordflow">if</span> (fp &lt;= Scalar(0.1) * delta) {</div>
<div class="line"><a name="l00216"></a><span class="lineno">  216</span>&#160;        par = 0;</div>
<div class="line"><a name="l00217"></a><span class="lineno">  217</span>&#160;        <span class="keywordflow">return</span>;</div>
<div class="line"><a name="l00218"></a><span class="lineno">  218</span>&#160;    }</div>
<div class="line"><a name="l00219"></a><span class="lineno">  219</span>&#160; </div>
<div class="line"><a name="l00220"></a><span class="lineno">  220</span>&#160;    <span class="comment">/* if the jacobian is not rank deficient, the newton */</span></div>
<div class="line"><a name="l00221"></a><span class="lineno">  221</span>&#160;    <span class="comment">/* step provides a lower bound, parl, for the zero of */</span></div>
<div class="line"><a name="l00222"></a><span class="lineno">  222</span>&#160;    <span class="comment">/* the function. otherwise set this bound to zero. */</span></div>
<div class="line"><a name="l00223"></a><span class="lineno">  223</span>&#160;    parl = 0.;</div>
<div class="line"><a name="l00224"></a><span class="lineno">  224</span>&#160;    <span class="keywordflow">if</span> (rank==n) {</div>
<div class="line"><a name="l00225"></a><span class="lineno">  225</span>&#160;        wa1 = qr.colsPermutation().inverse() *  diag.cwiseProduct(wa2)/dxnorm;</div>
<div class="line"><a name="l00226"></a><span class="lineno">  226</span>&#160;        qr.matrixQR().topLeftCorner(n, n).transpose().template triangularView&lt;Lower&gt;().solveInPlace(wa1);</div>
<div class="line"><a name="l00227"></a><span class="lineno">  227</span>&#160;        temp = wa1.blueNorm();</div>
<div class="line"><a name="l00228"></a><span class="lineno">  228</span>&#160;        parl = fp / delta / temp / temp;</div>
<div class="line"><a name="l00229"></a><span class="lineno">  229</span>&#160;    }</div>
<div class="line"><a name="l00230"></a><span class="lineno">  230</span>&#160; </div>
<div class="line"><a name="l00231"></a><span class="lineno">  231</span>&#160;    <span class="comment">/* calculate an upper bound, paru, for the zero of the function. */</span></div>
<div class="line"><a name="l00232"></a><span class="lineno">  232</span>&#160;    <span class="keywordflow">for</span> (j = 0; j &lt; n; ++j)</div>
<div class="line"><a name="l00233"></a><span class="lineno">  233</span>&#160;        wa1[j] = qr.matrixQR().col(j).head(j+1).dot(qtb.head(j+1)) / diag[qr.colsPermutation().indices()(j)];</div>
<div class="line"><a name="l00234"></a><span class="lineno">  234</span>&#160; </div>
<div class="line"><a name="l00235"></a><span class="lineno">  235</span>&#160;    gnorm = wa1.stableNorm();</div>
<div class="line"><a name="l00236"></a><span class="lineno">  236</span>&#160;    paru = gnorm / delta;</div>
<div class="line"><a name="l00237"></a><span class="lineno">  237</span>&#160;    <span class="keywordflow">if</span> (paru == 0.)</div>
<div class="line"><a name="l00238"></a><span class="lineno">  238</span>&#160;        paru = dwarf / (std::min)(delta,Scalar(0.1));</div>
<div class="line"><a name="l00239"></a><span class="lineno">  239</span>&#160; </div>
<div class="line"><a name="l00240"></a><span class="lineno">  240</span>&#160;    <span class="comment">/* if the input par lies outside of the interval (parl,paru), */</span></div>
<div class="line"><a name="l00241"></a><span class="lineno">  241</span>&#160;    <span class="comment">/* set par to the closer endpoint. */</span></div>
<div class="line"><a name="l00242"></a><span class="lineno">  242</span>&#160;    par = (std::max)(par,parl);</div>
<div class="line"><a name="l00243"></a><span class="lineno">  243</span>&#160;    par = (std::min)(par,paru);</div>
<div class="line"><a name="l00244"></a><span class="lineno">  244</span>&#160;    <span class="keywordflow">if</span> (par == 0.)</div>
<div class="line"><a name="l00245"></a><span class="lineno">  245</span>&#160;        par = gnorm / dxnorm;</div>
<div class="line"><a name="l00246"></a><span class="lineno">  246</span>&#160; </div>
<div class="line"><a name="l00247"></a><span class="lineno">  247</span>&#160;    <span class="comment">/* beginning of an iteration. */</span></div>
<div class="line"><a name="l00248"></a><span class="lineno">  248</span>&#160;    <a class="codeRef" href="../classEigen_1_1Matrix.html">Matrix&lt; Scalar, Dynamic, Dynamic &gt;</a> s = qr.matrixQR();</div>
<div class="line"><a name="l00249"></a><span class="lineno">  249</span>&#160;    <span class="keywordflow">while</span> (<span class="keyword">true</span>) {</div>
<div class="line"><a name="l00250"></a><span class="lineno">  250</span>&#160;        ++iter;</div>
<div class="line"><a name="l00251"></a><span class="lineno">  251</span>&#160; </div>
<div class="line"><a name="l00252"></a><span class="lineno">  252</span>&#160;        <span class="comment">/* evaluate the function at the current value of par. */</span></div>
<div class="line"><a name="l00253"></a><span class="lineno">  253</span>&#160;        <span class="keywordflow">if</span> (par == 0.)</div>
<div class="line"><a name="l00254"></a><span class="lineno">  254</span>&#160;            par = (std::max)(dwarf,Scalar(.001) * paru); <span class="comment">/* Computing MAX */</span></div>
<div class="line"><a name="l00255"></a><span class="lineno">  255</span>&#160;        wa1 = <a class="codeRef" href="../namespaceEigen.html#af4f536e8ea56702e63088efb3706d1f0">sqrt</a>(par)* diag;</div>
<div class="line"><a name="l00256"></a><span class="lineno">  256</span>&#160; </div>
<div class="line"><a name="l00257"></a><span class="lineno">  257</span>&#160;        <a class="codeRef" href="../classEigen_1_1Matrix.html">Matrix&lt; Scalar, Dynamic, 1 &gt;</a> sdiag(n);</div>
<div class="line"><a name="l00258"></a><span class="lineno">  258</span>&#160;        qrsolv&lt;Scalar&gt;(s, qr.colsPermutation().indices(), wa1, qtb, x, sdiag);</div>
<div class="line"><a name="l00259"></a><span class="lineno">  259</span>&#160; </div>
<div class="line"><a name="l00260"></a><span class="lineno">  260</span>&#160;        wa2 = diag.cwiseProduct(x);</div>
<div class="line"><a name="l00261"></a><span class="lineno">  261</span>&#160;        dxnorm = wa2.blueNorm();</div>
<div class="line"><a name="l00262"></a><span class="lineno">  262</span>&#160;        temp = fp;</div>
<div class="line"><a name="l00263"></a><span class="lineno">  263</span>&#160;        fp = dxnorm - delta;</div>
<div class="line"><a name="l00264"></a><span class="lineno">  264</span>&#160; </div>
<div class="line"><a name="l00265"></a><span class="lineno">  265</span>&#160;        <span class="comment">/* if the function is small enough, accept the current value */</span></div>
<div class="line"><a name="l00266"></a><span class="lineno">  266</span>&#160;        <span class="comment">/* of par. also test for the exceptional cases where parl */</span></div>
<div class="line"><a name="l00267"></a><span class="lineno">  267</span>&#160;        <span class="comment">/* is zero or the number of iterations has reached 10. */</span></div>
<div class="line"><a name="l00268"></a><span class="lineno">  268</span>&#160;        <span class="keywordflow">if</span> (<a class="codeRef" href="../namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">abs</a>(fp) &lt;= Scalar(0.1) * delta || (parl == 0. &amp;&amp; fp &lt;= temp &amp;&amp; temp &lt; 0.) || iter == 10)</div>
<div class="line"><a name="l00269"></a><span class="lineno">  269</span>&#160;            <span class="keywordflow">break</span>;</div>
<div class="line"><a name="l00270"></a><span class="lineno">  270</span>&#160; </div>
<div class="line"><a name="l00271"></a><span class="lineno">  271</span>&#160;        <span class="comment">/* compute the newton correction. */</span></div>
<div class="line"><a name="l00272"></a><span class="lineno">  272</span>&#160;        wa1 = qr.colsPermutation().inverse() * diag.cwiseProduct(wa2/dxnorm);</div>
<div class="line"><a name="l00273"></a><span class="lineno">  273</span>&#160;        <span class="comment">// we could almost use this here, but the diagonal is outside qr, in sdiag[]</span></div>
<div class="line"><a name="l00274"></a><span class="lineno">  274</span>&#160;        <span class="comment">// qr.matrixQR().topLeftCorner(n, n).transpose().template triangularView&lt;Lower&gt;().solveInPlace(wa1);</span></div>
<div class="line"><a name="l00275"></a><span class="lineno">  275</span>&#160;        <span class="keywordflow">for</span> (j = 0; j &lt; n; ++j) {</div>
<div class="line"><a name="l00276"></a><span class="lineno">  276</span>&#160;            wa1[j] /= sdiag[j];</div>
<div class="line"><a name="l00277"></a><span class="lineno">  277</span>&#160;            temp = wa1[j];</div>
<div class="line"><a name="l00278"></a><span class="lineno">  278</span>&#160;            <span class="keywordflow">for</span> (<a class="codeRef" href="../namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> i = j+1; i &lt; n; ++i)</div>
<div class="line"><a name="l00279"></a><span class="lineno">  279</span>&#160;                wa1[i] -= s(i,j) * temp;</div>
<div class="line"><a name="l00280"></a><span class="lineno">  280</span>&#160;        }</div>
<div class="line"><a name="l00281"></a><span class="lineno">  281</span>&#160;        temp = wa1.blueNorm();</div>
<div class="line"><a name="l00282"></a><span class="lineno">  282</span>&#160;        parc = fp / delta / temp / temp;</div>
<div class="line"><a name="l00283"></a><span class="lineno">  283</span>&#160; </div>
<div class="line"><a name="l00284"></a><span class="lineno">  284</span>&#160;        <span class="comment">/* depending on the sign of the function, update parl or paru. */</span></div>
<div class="line"><a name="l00285"></a><span class="lineno">  285</span>&#160;        <span class="keywordflow">if</span> (fp &gt; 0.)</div>
<div class="line"><a name="l00286"></a><span class="lineno">  286</span>&#160;            parl = (std::max)(parl,par);</div>
<div class="line"><a name="l00287"></a><span class="lineno">  287</span>&#160;        <span class="keywordflow">if</span> (fp &lt; 0.)</div>
<div class="line"><a name="l00288"></a><span class="lineno">  288</span>&#160;            paru = (std::min)(paru,par);</div>
<div class="line"><a name="l00289"></a><span class="lineno">  289</span>&#160; </div>
<div class="line"><a name="l00290"></a><span class="lineno">  290</span>&#160;        <span class="comment">/* compute an improved estimate for par. */</span></div>
<div class="line"><a name="l00291"></a><span class="lineno">  291</span>&#160;        par = (std::max)(parl,par+parc);</div>
<div class="line"><a name="l00292"></a><span class="lineno">  292</span>&#160;    }</div>
<div class="line"><a name="l00293"></a><span class="lineno">  293</span>&#160;    <span class="keywordflow">if</span> (iter == 0)</div>
<div class="line"><a name="l00294"></a><span class="lineno">  294</span>&#160;        par = 0.;</div>
<div class="line"><a name="l00295"></a><span class="lineno">  295</span>&#160;    <span class="keywordflow">return</span>;</div>
<div class="line"><a name="l00296"></a><span class="lineno">  296</span>&#160;}</div>
<div class="line"><a name="l00297"></a><span class="lineno">  297</span>&#160; </div>
<div class="line"><a name="l00298"></a><span class="lineno">  298</span>&#160;} <span class="comment">// end namespace internal</span></div>
<div class="line"><a name="l00299"></a><span class="lineno">  299</span>&#160; </div>
<div class="line"><a name="l00300"></a><span class="lineno">  300</span>&#160;} <span class="comment">// end namespace Eigen</span></div>
<div class="ttc" id="aclassEigen_1_1Matrix_html"><div class="ttname"><a href="../classEigen_1_1Matrix.html">Eigen::Matrix&lt; Scalar, Dynamic, Dynamic &gt;</a></div></div>
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